Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
528 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21448044 | C2 | semidirect |
| 3. #21447963 | C2 | semidirect |
| 4. #21447859 | C2 | semidirect |
| 5. Q8×#11758185 | C2 | semidirect |
| 6. C4×#14519720 | C2 | semidirect |
| 7. Q8×Q16×C61 | C2 | semidirect |
| 55. Q16×C61 | #41 | semidirect |
| 75. Q8×C61 | SD32 | semidirect |
| 103. Q8×Q16 | D61 | semidirect |
| 129. C61 | #33929 | semidirect |
| 161. Q16 | #11758226 | semidirect |
| 181. Q8 | #14519720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458794 | 2 |
| #21448044 | 2 |
| #21447963 | 2 |
| #21447859 | 2 |
| Q8×#11758185 | 2 |
| C4×#14519720 | 2 |
| Q8×Q16×C61 | 2 |
| #33929 | 61 |